2.01 - Introduction

On Sunday, 2003 November 23, a total eclipse of the Sun will be visible from a broad corridor that traverses portions of the Southern Hemisphere.
The path of the Moon's umbral shadow begins in the Indian Ocean, crosses Antarctica, and ends at sunrise near the edge of the southern continent.
A partial eclipse will be seen within the much broader path of the Moon's penumbral shadow, which includes Australia, New Zealand, Antarctica and southern South America (Figures 2.1 and 2.2 ).

The trajectory of the Moon's shadow takes it between the sunrise terminator and the South Pole.
As viewed from the Sun's direction, the Moon's shadow passes around the "back" side of the pole between Earth's axis of rotation and the terminator. Consequently, the track of totality travels east to west rather the usual west to east direction.
Furthermore, the 500 kilometer wide path both begins and ends at sunrise, just like the May 31 annular eclipse.
The unusual characteristics of these two events is directly attributed to their grazing geometries in Earth's polar regions coupled with the close temporal proximity of the eclipses with summer solstice in each hemisphere.

2.02 - Path of Totality

The path of the Moon's umbral shadow begins at 22:19 UT in the southern Indian Ocean about 1100 kilometers southeast of Kerguelen Island ( Figure 2.2 ).
Curving south, the five hundred kilometer wide umbral path reaches the coast of Antarctica at 22:35 UT.
The Shackleton Ice Shelf and Russia's Mirny research station lie in the path where the central duration is 1 minute 55 seconds and the Sun stands 13° above the frozen landscape.
Quickly moving inland, the elongated shadow sweeps over the desolate interior of the continent at velocities exceeeding 1 kilometer per second ( Figure 2.3 ).
No other permanently staffed research stations are encountered for the next half hour.

The instant of greatest eclipse1 occurs in Wilkes Land at 22:49:17 UT when the axis of the Moon's shadow passes closest to the center of Earth (gamma2 = -0.964).
At this point, the duration of totality reaches its maximum of 1 minute 55 seconds with a Sun altitude of 15°.
The duration and altitude slowly drop as the umbra's path curves from southwest to northwest.
The umbra reaches the Antarctic coast in Queen Maud Land, which harbors several more research stations (Novolazarevskaya, Maitri).
From Maitri, the 1 minute 19 second total phase occurs with the Sun just 2° above the horizon at 23:17 UT.

Two minutes later, the path ends and the shadow leaves Earth's surface (23:19 UT) one hour after it began.
Over the course of its sixty minute trajectory, the Moon's umbra sweeps over a track approximately 5,000 kilometers long and covering 0.51% of Earth's surface area.

The rest of Antarctica will see a partial eclipse as well as most of New Zealand, Australia, southern Argentina and Chile ( Figure 2.2).
Outside of Antarctica, southwestern Australia will witness the largest eclipse.
For instance, citizens of Perth will be treated to an early morning partial eclipse of magnitude 0.612.
In contrast, the Cape York Peninsula in northeastern Australia lies beyond the penumbra's path and will miss the eclipse entirely.

1 The instant of greatest eclipse occurs when the distance between the Moon's shadow axis and Earth's geocenter reaches a minimum.
Although greatest eclipse differs slightly from the instants of greatest magnitude and greatest duration (for total eclipses), the differences are usually quite small.

2.03 - Orthographic Map of the November 23 Eclipse Path

Figure 2.1 is an orthographic projection map of Earth [adapted from Espenak, 1987] showing the path of penumbral (partial) and umbral (total) eclipse.
The daylight terminator is plotted for the instant of greatest eclipse with north at the top.
The sub-Earth point is centered over the point of greatest eclipse and is indicated with an asterisk-like symbol.
The sub-solar point (Sun in zenith) at that instant is also shown.

The limits of the Moon's penumbral shadow define the region of visibility of the partial eclipse.
This saddle shaped region often covers more than half of Earth's daylight hemisphere and consists of several distinct zones or limits.
At the northern boundary lies the limit of the penumbra's path.
Great loops at the western and eastern extremes of the penumbra's path identify the areas where the eclipse begins/ends at sunrise and sunset, respectively.
Bisecting the 'eclipse begins/ends at sunrise and sunset' loops is the curve of maximum eclipse at sunrise (western loop) and sunset (eastern loop).
The exterior tangency points P1 and P4 mark the coordinates where the penumbral shadow first contacts (partial eclipse begins) and last contacts (partial eclipse ends) Earth's surface.
The path of the umbral shadow bisects the penumbral path from west to east and is shaded dark gray.

A curve of maximum eclipse is the locus of all points where the eclipse is at maximum at a given time.
They are plotted at each half hour Universal Time (UT), and generally run in a north-south direction.
The outline of the umbral shadow is plotted every ten minutes in UT.
Curves of constant eclipse magnitude3 delineate the locus of all points where the magnitude at maximum eclipse is constant.
These curves run exclusively between the curves of maximum eclipse at sunrise and sunset.
Furthermore, they are quasi-parallel to the northern penumbral limit and the umbral path of total eclipse.
The southern limit of the penumbra may be thought of as a curve of constant magnitude of 0%, while adjacent curves are for magnitudes of 20%, 40%, 60% and 80%.
The northern and southern limits of the path of total eclipse are curves of constant magnitude of 100%.

At the top of Figure 2.1 , the Universal Time of geocentric conjunction between the Moon and Sun is given followed by the instant of greatest eclipse.
The eclipse magnitude is given for greatest eclipse.
For central eclipses (both total and annular), it is equivalent to the geocentric ratio of diameters of the Moon and Sun.
Gamma is the minimum distance of the Moon's shadow axis from Earth's center in units of equatorial Earth radii.
The shadow axis passes south of Earth's geocenter for negative values of Gamma.
Finally, the Saros series number is given along with the eclipse's relative sequence in the series.

3 Eclipse magnitude is defined as the fraction of the Sun's diameter occulted by the Moon.
It is strictly a ratio of diameters and should not be confused with eclipse obscuration, which is a measure of the Sun's surface area occulted by the Moon.
Eclipse magnitude may be expressed as either a percentage or a decimal fraction (e.g.: 50% or 0.50).

2.04 - Stereographic Map of the November 23 Eclipse Path

The stereographic projection of Earth in Figure 2.2 depicts the path of penumbral and umbral eclipse in greater detail.
The map is oriented with north up.
International political borders are shown and circles of latitude and longitude are plotted at 20° increments.
The region of penumbral or partial eclipse is identified by its northern limit, curves of eclipse begins or ends at sunrise and sunset, and curves of maximum eclipse at sunrise and sunset.
Curves of constant eclipse magnitude are plotted for 20%, 40%, 60% and 80%, as are the limits of the path of total eclipse.
Also included are curves of greatest eclipse at every half hour Universal Time.

Figures 2.1 and 2.2 may be used to quickly determine the approximate time and magnitude of maximum eclipse at any location within the eclipse path.

2.05 - Detailed Maps of the Path of Totality

The path of totality is plotted on a detailed map appearing in Figure 2.3 .
The map uses coastline data from the World Data Bank II (WDBII).
The WDBII outline files are digitized from navigational charts to a working scale of approximately 1:3 million.
Major scientific research stations are plotted to show their relative positions with respect to the path of totality.
Only three of the several dozen stations actually lie within the track of total eclipse: Mirny, Novolazarevskaya, and Maitri.
Local circumstances have been calculated for the research stations and can be found in Table 2.6.

Although no corrections have been made for center of figure or lunar limb profile, they have little or no effect at this scale.
Atmospheric refraction4 has not been included because it depends on the atmospheric temperature-pressure profile, which cannot be predicted in advance.
These maps are also available on the web at http://sunearth.gsfc.nasa.gov/eclipse/TSE2003/TSE2003.html.

4 The nominal value for atmospheric refraction at the horizon is 34 arc-minutes, but this value can vary by a factor or 2 depending on atmospheric conditions.
For an eclipse in the horizon, the umbral path is shifted in the direction opposite from the Sun.

2.06 - Elements, Shadow Contacts and November 23 Eclipse Tables

The geocentric ephemeris for the Sun and Moon, various parameters, constants, and the Besselian
elements (polynomial form) are given in Table 2.1.
The eclipse elements and predictions were derived from
the DE200 and LE200 ephemerides (solar and lunar, respectively) developed jointly by the Jet Propulsion
Laboratory and the U. S. Naval Observatory for use in the Astronomical Almanac for 1984 and thereafter.
Unless otherwise stated, all predictions are based on center of mass positions for the Moon and Sun with no
corrections made for center of figure, lunar limb profile or atmospheric refraction.
The predictions depart from normal IAU convention through the use of a smaller constant for the mean lunar radius k for all
umbral contacts (see:
2.08 - Lunar Limb Profile for November 23).
Times are expressed in either Terrestrial Dynamical Time
(TDT) or in Universal Time (UT), where the best value of Delta T1 available at the time of preparation is used.

From the polynomial form of the Besselian elements, any element can be evaluated for any time t1
(in decimal hours) via the equation:

The polynomial Besselian elements were derived from a least-squares fit to elements rigorously calculated at
five separate times over a six hour period centered at t0.
Thus, the equation and elements are valid over the
period 20.00 ≤ t1 ≤ 02.00 TDT (Nov 23 to Nov 24).

Table 2.2 lists all external and internal contacts of penumbral and umbral shadows with Earth.
They include TDT times and geodetic coordinates with and without corrections for ΔT.
The contacts are defined:

Similarly, the noethern and southern extremes of the penumbral and umbral paths, and extreme limits of the umbra's central line are given.
The IAU (International Astronomical Union) longitude convention is used throughout this publication (i.e., for longitude, east is positive and west is negative; for latitude, north is positive and south is negative).

The path of the umbral shadow is delineated at two minute intervals in Universal Time in Table 2.3.
Coordinates of the northern limit, the southern limit and the central line are listed to the nearest tenth of an arc-minute (~185 m at the Equator).
The Sun's altitude, path width and umbral duration are calculated for the central line position.
Table 2.4 presents a physical ephemeris for the umbral shadow at two minute intervals in UT.
The central line coordinates are followed by the topocentric ratio of the apparent diameters of the Moon and Sun, the eclipse obscuration6, and the Sun's altitude and azimuth at that instant.
The central path width, the umbral shadow's major and minor axes and its instantaneous velocity with respect to Earth's surface are included.
Finally, the central line duration of the umbral phase is given.

Local circumstances for each central line position listed in Tables 2.3 and 2.4.
The first three columns give the Universal Time of maximum eclipse, the central line duration of totality and the altitude of the Sun at that instant. The following columns list each of the four eclipse contact times followed by their related contact position angles and the corresponding altitude of the Sun.
The four contacts identify significant stages in the progress of the eclipse. They are defined as follows:

First Contact

Instant of first external tangency between the Moon and Sun.
(partial eclipse begins)

Second Contact

Instant of first internal tangency between the Moon and Sun.
(central or umbral eclipse begins; total eclipse begins)

Third Contact

Instant of last internal tangency between the Moon and Sun.
(central or umbral eclipse ends; total eclipse ends)

Fourth Contact

Instant of last external tangency between the Moon and Sun.
(partial eclipse ends)

The position angles P and V identify the point along the Sun's disk where each contact occurs7.
Second and third contact altitudes are omitted since they are always within 1° of the altitude at maximum eclipse.

7P is defined as the contact angle measured counter-clockwise from the north point of the Sun's disk.
V is defined as the contact angle measured counter-clockwise from the zenith point of the Sun's disk.

2.07 - Local Circumstances Tables for November 23

Local circumstances for ~140 cities and locations in Antarctica, Australia, New Zealand and South America are presented in Tables 2.6 through 2.10.
These tables give the local circumstances at each contact and at maximum eclipse1 for every location.
The coordinates are listed along with the location's elevation (meters) above sea-level, if known.
The Universal Time of each contact is given to a tenth of a second, along with position angles P and V and the altitude of the Sun.
The position angles identify the point along the Sun's disk where each contact occurs and are measured counter-clockwise (i.e., eastward) from the north and zenith points, respectively.
Locations outside the umbral path miss the umbral eclipse and only witness first and fourth contacts.
The Universal Time of maximum eclipse (either partial or total) is listed to a tenth of a second.
Next, the position angles P and V of the Moon's disk with respect to the Sun are given, followed by the altitude and azimuth of the Sun at maximum eclipse.
Finally, the corresponding eclipse magnitude and obscuration are listed.
For total eclipses, the eclipse magnitude is identical to the topocentric ratio of the Moon's and Sun's apparent diameters.

Two additional columns are included if the location lies within the path of the Moon's umbral shadow.
The umbral depth is a relative measure of a location's position with respect to the central line and path limits.
It is a unitless parameter which is defined as:

u = 1 - abs(x/R) [1]

where:

u

=

umbral depth

x

=

perpendicular distance from the shadow axis (kilometers)

R

=

radius of the umbral shadow as it
intersects Earth's surface (kilometers)

The umbral depth for a location varies from 0.0 to 1.0.
A position at the path limits corresponds to a value of 0.0 while a position on the central line has a value of 1.0.
The parameter can be used to quickly determine the corresponding central line duration.
Thus, it is a useful tool for evaluating the trade-off in duration of a location's position relative to the central line.
Using the location's duration and umbral depth, the central line duration is calculated as:

D =
d/(1 - (1 - u)2)1/2
seconds [2]

where:

D

=

duration of totality on the center line
(seconds)

d

=

duration of totality at location (seconds)

u

=

umbral depth

The final column gives the duration of totality.
The effects of refraction have not been included in these calculations, nor have there been any corrections for center of figure or the lunar limb profile.

The geographic coordinates of cities are from The New International Atlas (Rand McNally, 1991).
Coordinates in Antarctica are from
www.scar.org/Antarctic%20Info/wintering_stations_2000.htm.
The city names and spellings presented here are for location purposes only and are not meant to be authoritative.
They do not imply recognition of status of any location by the United States Government.

8 For partial eclipses, maximum eclipse is the instant when the greatest fraction of the Sun's diameter is occulted.
For total eclipses, maximum eclipse is the instant of mid-totality.

9Eclipse magnitude is the fraction of the Sun's diameter occulted by the Moon, while eclipse obscuration is the fraction of the Sun's surface area occulted by the Moon.

2.08 - Lunar Limb Profile for November 23

Eclipse contact times, magnitude and duration of totality all depend on the angular diameters and relative velocities of the Moon and Sun.
These calculations are limited in accuracy by the departure of the Moon's limb from a perfectly circular figure.
The Moon's surface exhibits a rather dramatic topography, which manifests itself as an irregular limb when seen in profile.
Most eclipse calculations assume some mean radius that averages high mountain peaks and low valleys along the Moon's rugged limb.
Such an approximation is acceptable for many applications, but if higher accuracy is needed, the Moon's actual limb profile must be considered.
Fortunately, an extensive body of knowledge exists on this subject in the form of Watts' limb charts [Watts, 1963].
These data are the product of a photographic survey of the marginal zone of the Moon and give limb profile heights with respect to an adopted smooth reference surface (or datum).
Analyses of lunar occultations of stars by Van Flandern [1970] and Morrison [1979] have shown that the average cross-section of Watts' datum is slightly elliptical rather than circular.
Furthermore, the implicit center of the datum (i.e., the center of figure) is displaced from the Moon's center of mass.
Additional work by Morrison and Appleby [1981] shows that the radius of the datum varies with libration producing systematic errors in Watts' original limb profile heights that attain 0.4 arc-seconds at some position angles.
Thus, corrections to Watts' limb data are necessary to ensure that the reference datum is a sphere with its center at the center of mass.

The Watts charts have been digitized and may be used to generate limb profiles for any libration.
Ellipticity and libration corrections can be applied to refer the profile to the Moon's center of mass.
Such a profile can then be used to correct eclipse predictions which have been generated using a mean lunar limb.

The lunar limb profile in Figure 2.4 includes corrections for center of mass and ellipticity [Morrison and Appleby, 1981].
It is generated for the central line at 22:40 UT, which is close to Russia's Mirny research base.
The Moon's topocentric libration (physical + optical) is l=+0.21° b=+0.29°, and the topocentric semi-diameters of the Sun and Moon are 971.8 and 1008.4 arc-seconds, respectively.
The Moon's angular velocity with respect to the Sun is 0.632 arc-seconds per second.

The radial scale of the limb profile (bottom of Figure 2.4) is greatly exaggerated so that the true limb's departure from the mean lunar limb is readily apparent.
The mean limb with respect to the center of figure of Watts' original data is shown (dashed) along with the mean limb with respect to the center of mass (solid).
Note that all the predictions presented in this publication are calculated with respect to the latter limb unless otherwise noted.
Position angles of various lunar features can be read using the protractor marks along the Moon's mean limb (center of mass).
The position angles of second and third contact are clearly marked along with the north pole of the Moon's axis of rotation and the observer's zenith at mid-totality.
The dashed line with arrows at either end identifies the contact points on the limb corresponding to the northern and southern limits of the path.
To the upper left of the profile are the Sun's topocentric coordinates at maximum eclipse.
They include the right ascension R.A., declination Dec., semi-diameter S.D.
and horizontal parallax H.P.
The corresponding topocentric coordinates for the Moon are to the upper right.
Below and left of the profile are the geographic coordinates of the center line at 22:40 UT while the times of the four eclipse contacts at that location appear to the lower right.
Directly below the profile are the local circumstances at maximum eclipse.
They include the Sun's altitude and azimuth, the path width, and central duration.
The position angle of the path's northern/southern limit axis is PA(N.Limit) and the angular velocity of the Moon with respect to the Sun is A.Vel.(M:S).
At the bottom left are a number of parameters used in the predictions, and the topocentric lunar librations appear at the lower right.

In investigations where accurate contact times are needed, the lunar limb profile can be used to correct the nominal or mean limb predictions.
For any given position angle, there will be a high mountain (annular eclipses) or a low valley (total eclipses) in the vicinity that ultimately determines the true instant of contact.
The difference, in time, between the Sun's position when tangent to the contact point on the mean limb and tangent to the highest mountain (annular) or lowest valley (total) at actual contact is the desired correction to the predicted contact time.
On the exaggerated radial scale of Figure 2.4, the Sun's limb can be represented as an epicyclic curve that is tangent to the mean lunar limb at the point of contact.
Using the digitized Watts' datum, an analytical solution is straightforward and robust.
Curves of corrections to the times of second and third contact for most position angles have been computer generated and plotted.
The circular protractor scale at the center represents the nominal contact time using a mean lunar limb.
The departure of the contact correction curves from this scale graphically illustrates the time correction to the mean predictions for any position angle as a result of the Moon's true limb profile.
Time corrections external to the circular scale are added to the mean contact time; time corrections internal to the protractor are subtracted from the mean contact time.
The magnitude of the time correction at a given position angle is measured using any of the four radial scales plotted at each cardinal point.

For example, Table 2.6 gives the following data for he Antarctic base Mirny:

The above corrected values are within 0.1 seconds of a rigorous calculation using the true limb profile.

2.09 - Sky During Totality

The total phase of an eclipse is accompanied by the onset of a rapidly darkening sky whose appearance resembles evening twilight about half an hour after sunset.
The effect presents an excellent opportunity to view planets and bright stars in the daytime sky.
Aside from the sheer novelty of it, such observations are useful in gauging the apparent sky brightness and transparency during totality.

During the total solar eclipse of 2003, the Sun is in northern Scorpius near the border with Libra.
From Antarctica, three naked eye planets and a number of bright stars will be above the horizon within the umbral path.
Figure 2.5 depicts the appearance of the sky during totality as seen from the central line at 22:40 UT.
This is close to Russia's Mirny research base, where the early morning eclipse occurs low in the southeastern sky.

The most conspicuous planet visible during totality will be Venus (mv=-3.8) located 25° east of the Sun in Ophiuchus.
Mercury (mv=-0.4) lies between the Sun and Venus at a solar elongation of 16° east.
Jupiter (mv=-1.8) is over a magnitude brighter than Mercury but it will be located in Leo in the northeastern sky 75° away from the Sun.
From the central line at 22:40 UT, Venus, Mercury and Jupiter will have altitudes above the horizon of 9.4°, 12.6° and 12.7°, respectively.
For comparison, the Sun's altitude will be 14°.
Saturn and Mars are both be below the horizon.

A number of the bright stars may also be visible it the twilight sky during the total eclipse.
Antares (mv=+1.06) is 10° southeast of the Sun.
The great southern stars Alpha (mv=+0.14) and Beta (mv=+0.58) Centauri are high in the sky about 44° from the Sun.
Canopus is near the zenith about 100° away and Achernar (mv=+0.45) stands high in the southwest.
Sirius (mv=-1.44) and the bright stars of Orion lie in the northwest quadrant of the sky.
It should be noted that star visibility requires a very dark and cloud free sky during totality.

The following ephemeris [using Bretagnon and Simon, 1986] gives the positions of the naked eye planets during the eclipse.
Delta is the distance of the planet from Earth (A.U.'s), App. Mag. is the apparent visual magnitude of the planet, and Solar Elong gives the elongation or angle between the Sun and planet.